The stress field and energy of screw dislocation in smectic A liquid crystals and the mistakes of the classical solution

The mistakes in the classical solution of a screw dislocation in smectic A liquid crystals are pointed out. A serious problem with the well-known theory is pointed, which may be named de Gennes-Kleman-Pershan paradox and has existed for many decades in the scientific community of liquid crystal study. The correct solution is given in this paper by a simplest, elementary, and straight forward method. In connection with this, the stress field and energy of dislocation are discussed in detail. The present article provides the correct stress field and dislocation energy as well.